Average Error: 0.5 → 0.5
Time: 2.2s
Precision: 64
\[\sqrt{x - 1} \cdot \sqrt{x}\]
↓
\[\sqrt{x - 1} \cdot \sqrt{x}\]
\sqrt{x - 1} \cdot \sqrt{x}
↓
\sqrt{x - 1} \cdot \sqrt{x}
double f(double x) {
        double r1774 = x;
        double r1775 = 1.0;
        double r1776 = r1774 - r1775;
        double r1777 = sqrt(r1776);
        double r1778 = sqrt(r1774);
        double r1779 = r1777 * r1778;
        return r1779;
}
↓
double f(double x) {
        double r1780 = x;
        double r1781 = 1.0;
        double r1782 = r1780 - r1781;
        double r1783 = sqrt(r1782);
        double r1784 = sqrt(r1780);
        double r1785 = r1783 * r1784;
        return r1785;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[\sqrt{x - 1} \cdot \sqrt{x}\]

  2. Final simplification0.5

    \[\leadsto \sqrt{x - 1} \cdot \sqrt{x}\]

Reproduce

herbie shell --seed 2020001 
(FPCore (x)
  :name "sqrt times"
  :precision binary64
  (* (sqrt (- x 1)) (sqrt x)))